Calculating Work for Displacement of Floating Cylinder

[bcjochim07]

Homework Statement

A 4 cm diameter cylinder floats in the water. How much work must be done to push the cylinder 10 cm deeper into the water?

Homework Equations

The Attempt at a Solution

I did the integral from 0 to .1 m of (.02m)^2 * pi * (1000kg/m^3) * (9.80) * x dx

= (12.3 x^2)/2 evaluated from 0 to .1 = .0615 J. However, the back of my book says .615 J. Somehow I ended up a decimal place off. Could someone help me?

 

[bcjochim07]

Anyone have any thoughts on this one?

 

[jimvoit]

Isn't the radius=0.2 instead of 0.02 ?

 

[bcjochim07]

no, I'm pretty sure the radius is correct

4 cm/2 = radius of 2 cm 2cm * 1m/100cm = .02 m

 

[bcjochim07]

Any thoughts would be greatly appreciated

 

[jimvoit]

I think that given the values you are working with that your answer is correct.

 

[bcjochim07]

I am concerned because the back of my book says it's .615 J and I can't figure out what's wrong with mine

 

[bcjochim07]

Can somebody find my mistake?

 

[bcjochim07]

I need some help with this one pretty soon because my homework is due tomorrow. Thanks!

 

[jimvoit]

Sometimes the answer in the book is wrong...or the problem data has been misread. In either case it looks like to me that your answer is correct, If not, I would also like to know why and maybe another reader can set us both strait.